Problem: Simplify the following expression: $k = \dfrac{40r + 60}{50r - 50q} + \dfrac{50p + 30}{50r - 50q}$ You can assume $p,q,r \neq 0$.
Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{40r + 60 + 50p + 30}{50r - 50q}$ $k = \dfrac{40r + 90 + 50p}{50r - 50q}$ The numerator and denominator have a common factor of $10$, so we can simplify $k = \dfrac{4r + 9 + 5p}{5r - 5q}$